An analytical investigation of steady-state flutter of the hereditary deformable plates in supersonic flow field

This article deals with an analytical investigation of steady-state flutter of a closed cylindrical body placed in a supersonic flow field, which has hereditary-deformable characteristics. For simplicity, two-dimensional aerodynamic flow is considered. The structural model is represented by the integro-differential equation. Aerodynamic model of the problem is based on the aerodynamic piston theory. Bubnov-Galerkin method is used to discretize partial differential equation of motion of the plate. The influence of relaxation parameters on the plate modal frequencies and critical flutter speed is examined analytically. The relaxation parameters and hereditary properties of the material are found to have opposite effects on the time evolution of the panel frequency and critical speed. The analytical solution of steady-state flutter is obtained for the first time for hereditary-deformable shell and flat plate